This is interesting. May I ask for a clarification? I assume that this sequence is produced with a greedy algorithm; that is, having disposed of all the natural numbers below k, we incorporate the smallest sum k + ... + (k+n) that is the only nontrivial trapezoidal representation of that sum. If we reach a point where there is no such sum, then the sequence ends. We do not backtrack, looking for the lexicographically earliest infinite sequence of unique sums. We conjecture that the greedy sequence does not end. Have I got all that right? None of the obvious related sequences are in OEIS yet: the lengths of the blocks 2,2,2,3,4,2,16,..., the starting numbers 1,3,5,7,10,14,16,..., the ending numbers 2,4,6,9,13,15,31,.... I think a crucial insight is that the allowable sums are numbers with exactly one nontrivial odd divisor, that is, numbers of the form p*2^n, p>1. This means that there are two more associated sequences; the sequence of p (3,7,11,3,23,29,47,...) and the sequence of n (0,0,0,3,1,0,3,1,0,...); neither of these are in OEIS. On Fri, Aug 14, 2020 at 7:47 PM Éric Angelini <eric.angelini@skynet.be> wrote:
Hello Math-fun, could I recommend to our members who like erratic behaviors to have a look at http://oeis.org/A336897 Best, É. Catapulté de mon aPhone
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